Questions tagged [kinetic-theory-of-gases]

Questions about the assumptions, equations, and properties of gases derived from kinetic theory. For questions pertaining to rates of reactions, please use the kinetics tag instead.

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-3 votes
0 answers
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Calculating the mean free path using the mean square displacement [closed]

I want to obtain the mean free path of a gas by using the mean square displacement, which I have calculated with the formula $$MSD= 2 \cdot D \cdot t$$ where $D$ is the diffusion coefficient of the ...
-2 votes
1 answer
184 views

Average molecular distance between hydrogen gas [closed]

The whole question goes like this: Calculate the de Broglie wavelength of hydrogen molecule at 300K (Take the translational energy to be 1.5kT) Compare this to the average intermolecular spacing for ...
2 votes
0 answers
73 views

What is the average collision duration?

So I've been trying to figure this out: What is the average collision duration of a gas in terms of macroscopic variables? What I have figured out. Whenever two molecules collide they must reach a ...
8 votes
1 answer
474 views

Confusion in Van der Waals Equation

I understand that the behavior of ideal gases deviates largely from that of real gases in terms of pressure exerted by the gas molecules on the container in which it is present, space available for ...
0 votes
0 answers
36 views

What ideal gas behavior is observed by a real gas that observes Boyle's law (at Boyle's temperature)?

Boyle's temperature is a constant for a particular gas. At this temperature the real gas behaves ideally. So, does the real gas only follow Boyle's law at this temperature, or are all the gas laws ...
11 votes
1 answer
1k views

Why does gas particle velocity affect rate of effusion?

I understand why smaller particles have more velocity, but I don't understand what velocity has to do with the rate of effusion: My reasoning is thus: Pressure is the number of impacts of particles ...
0 votes
0 answers
35 views

Does KE(avg) stay the same for ideal gas if the PV value changes?

We know that Kinetic Energy is a function of Temperature for an ideal gas. So KE (1 Mole of gas) = (3/2)RT = (3/2)PV. So it's said that even if P or V change their change will counteract the other (...
0 votes
2 answers
176 views

Why do we subtract the volume correction term in the van der Waals gas equation [duplicate]

The following equation is valid for ideal gasses $$pV=nRT$$ Please mind the following notation, any parameter that is related to an ideal gas would be denoted with a subscript $i$ and anything related ...
0 votes
1 answer
313 views

Cubic nature of van der Waals' gas equation

$V_m^3-\dfrac{RT+bP}{P}V_m^2+\dfrac{a}{P}V_m-\dfrac{ab}{P}=0$ So, At $T<T_c$ the above equation has three real roots say $V_1,V_2,V_3$, my doubt is what does this mean physically because for some ...
3 votes
2 answers
9k views

What is the relation between absolute temperature, and rates of diffusion and effusion of a gas?

According to Graham's diffusion law, rate of diffusion is directly proportional to square root of temperature but rate of effusion is inversely proportional to square root of temperature. Why is this ...
1 vote
1 answer
190 views

Question on Thermodynamics from a recently conducted Examination

This is a question from the recently conducted JEE Main exam (in India). I had solved it myself, but found the answer to be incorrect. Here's the question. Here is how I solved it: $\Delta H = \pu{41....
-2 votes
1 answer
37 views

Isolation is a Consequence of Definition [closed]

Let's consider a ballon, such that it has an adiabatic wall, and there is no exchange of heat with the surroundings. Now, let the balloon wall be completely impermeable to the movement of matter ...
6 votes
2 answers
7k views

Latent Heat and Kinetic Energy

The kinetic theory says that temperature is the measure of the average kinetic energy. That would mean then: The temperature rises with the rise in kinetic energy. We know that when matter changes ...
0 votes
1 answer
111 views

According to Maxwell-Boltzmann distribution, what is probability distribution function proportional to?

If, according to the Maxwell-Boltzmann distribution $${f(v)}\propto\exp\left(-\frac{\varepsilon}{kT}\right),\tag{1}$$ which is the equation from which the whole final equation is derived, then why is ...
2 votes
1 answer
2k views

Finding root-mean-square speed of neon using kinetic energy

Find the root-mean-square speed of $\ce{Ne}$ atoms at the temperature at which their kinetic energy is $\pu{6.24 kJ mol-1}.$ I tried using the kinetic energy formula $$\mathrm{KE} = \frac{mv^2}{2},$$ ...
1 vote
1 answer
155 views

If Graham's law doesn't apply to the ammonia and hydrogen chloride diffusion in a glass tube demonstration, is there a law that does?

A comment below What exactly are "white fumes" and why does holding a bottle of ammonia (conc) next to a bottle of HCl (conc) make them? links to The Royal Society Of Chemistry video ...
9 votes
3 answers
834 views

Comparing van der Waals constant for gases

How can I compare the van der Waals constant $a$ (the liquefication constant) for different compounds based on my knowledge of bonding in the compound? Let's pick the following sample set: $$ \...
1 vote
1 answer
126 views

Why is the value of $A$, in the expression for Boltzmann's distribution of speeds, not directly calculated?

I've read the proof for the expression for Boltzmann's distribution of speeds on this site. There, $f(v)$ is first factorized into $f(v_x)$, $f(v_y)$ and $f(v_z)$ and $A$ into $A_x$, $A_y$ and $A_z$. ...
4 votes
0 answers
62 views

Why does the factor of ⅔ come in when we calculate net flux due to diffusion for an ideal gas

As per Atkins' Physical Chemistry (11E) Pg:694. We arrive at a crude estimate for the net flux through an imaginary flux plane. We find it to be $$J_{z}=-\frac{1}{2}v_{mean}\lambda(\frac{d\mathcal{N}}{...
2 votes
1 answer
281 views

Relation between concentration and activation energy

Will increasing the concentration of the reactants in a chemical reaction increase the proportion of molecules with an energy greater than the activation energy $E_\mathrm{a}$? It seems to me that the ...
0 votes
1 answer
87 views

What is heat bath here?

At the beginning $\pu{1 mol}$ of air is compressed to $\pu{3 atm}$ at a of temperature $\pu{523 K}$. After a random process, the pressure of the air equates to $\pu{1 bar}$ at a temperature of $\pu{...
1 vote
1 answer
99 views

Density gradient vs. entropy of mixing

I was wondering how real gases would behave when they are released into a closed container with fixed volume. For example, suppose we use chlorine and nitrogen gas. Obviously, chlorine has a higher ...
5 votes
2 answers
30k views

Is internal energy equal to (3/2)nRT for an ideal monoatomic gas?

I came across a Khan Academy video providing the following relation for the internal energy of the system $U$: $$U=\frac32nRT,\label{eqn:1}\tag{1}$$ where $n$ is the amount of gas, $R$ is the ...
0 votes
1 answer
578 views

Degrees of freedom of a molecule of N atoms [closed]

Apparently a molecule of N atoms has 3N degrees of freedom. How? Shouldn't it be dependent on the structure of the molecule? How exactly do we derive this?
3 votes
1 answer
129 views

How was it possible to accurately measure the mass of gases in the 19th century?

I have seen periodic tables of Mendeleev (1834-1907) and Newland (1837-1898) in which masses of gases such as oxygen and nitrogen were shown. I don't think there were instruments to measure mass of ...
3 votes
2 answers
1k views

Is air made 100% from atoms?

I know air is made up of roughly 78% nitrogen, 20% oxygen, etc.. but I would like to know what percentage of air is just space and has no atoms at all.
0 votes
1 answer
142 views

Confusion regarding continuity of state

I was reading about Andrew's isotherms and about the continuity of state. What confused me was the continuous conversion of gaseous state to liquid state. Now my textbook says that by keeping volume ...
3 votes
0 answers
97 views

Formula for collision frequency and mean free path

We were studying collision frequency and mean free path today, and in it, we got the equations of collision frequency as: $$Z=\sqrt 2 \pi \sigma^2v_{rms}N$$ where $N$ is the number density, equal to $...
0 votes
0 answers
71 views

Is the value for the Boltzmann Constant different in 2D?

So I'm simulating some hard sphere collisions and want to determine the Boltzmann constant in two dimension, using the equation $$PA=Nk_BT$$ where $A=\pi R^2_{container}$, $P=(averageImpulse/time)/(2\...
1 vote
0 answers
108 views

Virial expansion of real gas equation and volume work

Hi I am currently working on a thermodynamics problem, and it asks me to first find the volume work done on a gas that behaves like the simplified Dieterici equation (see below) predicts on isothermal ...
18 votes
6 answers
7k views

Does the Maxwell-Boltzmann distribution apply to gases only?

The Maxwell-Boltzmann distribution can be used to determine the fraction of particles with sufficient energy to react. I know that the curve applies to gaseous reactants and would like to know whether ...
2 votes
0 answers
57 views

Is this a valid interpretation of the Mean relative speed between two (Maxwell-Boltzmann) species?

In textbooks, the collision frequency $Z_{ab}$ is always given as something like: $$Z_{ab} = n_an_b\sigma_{ab} \Bigg(\frac{8 k T}{\pi \mu}\Bigg)^{1/2}= n_an_b\sigma_{ab} \bar{C}_{rel}$$ where the ...
3 votes
0 answers
158 views

What exactly is a photon gas?

I came upon this question in a JEE Advanced mock test online: The number of photons of wavelength $\lambda$ required to achieve pressure $P$ in an empty cubical box of edge length $l$ is given by $\...
4 votes
1 answer
136 views

Rigorous reason behind internal energy change being zero while mixing

A container is divided in two parts: one part contains oxygen gas $(n_1$ moles, at temperature $T_1)$ and the other part contains helium gas $(n_2$ moles, at temperature $T_2).$ The partition ...
8 votes
1 answer
1k views

Contribution of vibrational degrees of freedom in linear triatomic molecule

The ratio $\displaystyle\frac{C_p}{C_v}$ for linear triatomic molecules including vibration contribution is given by ____. Attempt: We are aware that $C_v = \frac{fR}{2}$ and $C_p = C_v+ R$ Hence, $\...
5 votes
3 answers
4k views

Kinetic energy of molecules in liquid state?

My book (book link) has this question: The kinetic energy of molecules at constant temperature in gaseous state is: more than those in the liquid state less than those in the liquid ...
1 vote
1 answer
208 views

Change in pressure?

Consider a sample of gas in a fixed volume container . From the arguments of Kinetic Theory of Gases on quadrupling the temperature what will be the effect on pressure . Basically I thought that the ...
1 vote
1 answer
839 views

Does lowering temperature of a gas make it easier to compress?

My teacher said that for ideal gases, the lower the temperature, the lower the kinetic energy of a gas will be, and it will be easier to compress the gas. Using the ideal gas equation $PV=nRT$, if ...
9 votes
1 answer
31k views

Derivation of mean speed from Maxwell–Boltzmann distribution

I found that if a velocity of a gas follows the Maxwell–Boltzmann distribution, the mean velocity is given by $$\langle v \rangle = \sqrt{\frac{8RT}{\pi M}}$$ where $R$ is the gas constant, $T$ is ...
11 votes
3 answers
30k views

Reason for negative Joule Thomson coefficient of Helium and Hydrogen at NTP conditions

Recently, while reading my textbook I came to know that Helium, Hydrogen and Neon are the only gases which have negative Joule Thomson coefficient at NTP conditions, i.e heating effect is observed ...
-2 votes
1 answer
2k views

Maximum in Maxwell–Boltzmann distribution [closed]

I need to find the velocity at which the fraction is maximum in Maxwell–Boltzmann distribution $$P(v) = \left(\frac{m}{2\pi kT}\right)^{\frac{3}{2}}4\pi v^2 \exp{\left(-\frac{mv^2}{2kT}\right)}$$ I ...
0 votes
0 answers
55 views

Which formula for kinetic energy of 1 mol of a gas is universally applicable? [duplicate]

I have read 2 formulas for kinetic energy of 1 mol of gas - 3/2 RT and 1/2fRT . But if I equate them then f comes out to be 3 . But f is different of mono, di, polyatomic gases . Where am I wrong in ...
-2 votes
1 answer
81 views

Graham's Law of Effusion when Looking at Samples with Equal Mass?

So, I had a question on a chemistry test about two gas samples, one of O2 and one of N2, that had equal masses. We were given the time of effusion for the sample of N2 and then asked to calculate the ...
1 vote
2 answers
1k views

Change in Enthalpy in Free Expansion of Ideal and Real gas against Vacuum

By free expansion, I am referring to gas allowed to expand freely against vacuum in a Joule Expansion. If gas is ideal then change in Internal Energy '∆U' and change in Enthalpy '∆H' is zero. (By ∆H = ...
8 votes
5 answers
2k views

Is the average kinetic energy of evaporating water molecules (at room temperature) equivalent to the average kinetic energy of boiling water?

Purpose: On new year's eve, after a splendid red and an assortment of sumptuous repasts, I made a bold remark which, on further consideration, may turn out to be incorrect. Unless! Unless I can ...
2 votes
3 answers
923 views

Why is the speed of ideal gases mass dependent while the kinetic energy is not?

The rms speed of an ideal gas is $v_{\text{rms}}$ = $\sqrt{\frac{3RT}{M} }$ and the kinetic energy is $E_\text{k} = \frac32RT$. From this, it is concluded that the speed is mass dependent, while the ...
3 votes
1 answer
130 views

Question regarding $Z$ (Compressibility factor)

Oh! This problem has been bugging me for a long time. According to Wikipedia, the Compressibility factor $Z$ is defined as the ratio of the volume occupied by a real gas to the volume occupied by an ...
-1 votes
2 answers
361 views

Why are some liquids hotter than room temperature gases if liquid and solid molecules move more slowly than gases? [closed]

We learned in school that state change is a matter of molecules moving faster and faster. And we learned "heat em up, speed em up, spread em out". Why then can some liquids have higher ...
-1 votes
2 answers
2k views

Under what conditions does Real Gases show Ideal Behaviour? [closed]

MY textbook says : Real gases show Ideal Behavior under low pressure ,high temperature. So I wanted to know what happens to real gases at high pressure ,low pressure Do they also show ideal behavior ...
6 votes
1 answer
37k views

Calculating Compressibility factor from the Van der Waals' Gas equation

So this problem has been bugging me for a long time. According to Wikipedia the compressibility factor $Z$ is defined as the ratio of the volume occupied by a real gas divided by the volume occupied ...